Solve 1+2x/3>x-1

$$\frac { 1 + 2 x } { 3 } > x - 1$$

Solve for x

$$x<4$$

Solution Steps

Multiply both sides of the equation by 3. Since 3 is positive, the inequality direction remains the same.

$$1+2x>3x-3$$

Subtract 3x from both sides.

$$1+2x-3x>-3$$

Combine 2x and -3x to get -x.

$$1-x>-3$$

Subtract 1 from both sides.

$$-x>-3-1$$

Subtract 1 from -3 to get -4.

$$-x>-4$$

Divide both sides by -1. Since -1 is negative, the inequality direction is changed.

$$x<\frac{-4}{-1}$$

Fraction \frac{-4}{-1} can be simplified to 4 by removing the negative sign from both the numerator and the denominator.

$$x<4$$